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A081502
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Let n = 10x + y where 0 <= y <= 9, x >= 0. Then a(n) = 3x+y.
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10
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0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 21, 22, 23, 24, 25, 26, 27, 28, 29
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OFFSET
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0,3
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COMMENTS
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Eswaran observes that n is divisible by 7 iff repeated application of a ends at the number 7.
a(n) is divisible by 7 iff n is divisible by 7: e.g., a(7) = a(14) = a(21) = 7, a(28) = a(35) = a(42) = 14 etc. - Zak Seidov, Mar 19 2014
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REFERENCES
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R. Eswaran, Test of divisibility of the number 7, Abstracts Amer. Math. Soc., 23 (No. 2, 2002), #974-00-5, p. 275.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,1,-1).
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FORMULA
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G.f.: -x*(6*x^9-x^8-x^7-x^6-x^5-x^4-x^3-x^2-x-1) / (x^11-x^10-x+1). - Colin Barker, Mar 19 2014
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MAPLE
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local x, y ;
y := modp(n, 10) ;
x := iquo(n, 10) ;
3*x+y ;
end proc:
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MATHEMATICA
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Table[n - 7 * Floor[n / 10], {n, 0, 100}] (* Joshua Oliver, Dec 04 2019 *)
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PROG
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(PARI) a(n) = [3, 1]*divrem(n, 10); \\ Kevin Ryde, Dec 04 2019
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CROSSREFS
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Different from A028898 for n>=100 (e.g. a(111) = 34, A029989(111) = 13).
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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